document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1033300>Question 1033300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the given information to determine the exact trigonometric value.<BR>\n" );
document.write( "If csc(theta)= -5/2 and 180 degrees < theta < 270 degrees; find the exact value of sin(2theta) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #647900 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=647900\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Use the given information to determine the exact trigonometric value.<BR>\n" );
document.write( "If csc(theta)= -5/2 and 180 degrees < theta < 270 degrees; find the exact value of sin(2theta) <BR>\n" );
document.write( "------<BR>\n" );
document.write( "Note: sin = 1/csc, so sin(t) = y/r = -2/5<BR>\n" );
document.write( "In QIII, y is negative.<BR>\n" );
document.write( "So, y = -2 and r = 5<BR>\n" );
document.write( "Then x = -sqrt[5^2-2^2] = -sqrt[21]<BR>\n" );
document.write( "and cos(x) = -sqrt(21)/5<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Ans: sin(2t) = 2*sin(t)cos(5) = 2(-2/5)(-sqrt(21)/5) = -(4/25)sqrt(21)<BR>\n" );
document.write( "============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "stan H.<BR>\n" );
document.write( "------------  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );